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SUMMARY:Byungchul Cha (Muhlenberg College)
DTSTART:20201106T171500Z
DTEND:20201106T183000Z
DTSTAMP:20260423T021419Z
UID:NEDNT/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/8/">In
 trinsic Diophantine Approximation of circles</a>\nby Byungchul Cha (Muhlen
 berg College) as part of New England Dynamics and Number Theory Seminar\n\
 nLecture held in Online.\n\nAbstract\nLet $S^1$ be the unit circle in $\\m
 athbb{R}^2$ centered at the origin and let $Z$ be a countable dense subset
  of $S^1$\, for instance\, the set $Z = S^1(\\mathbb{Q})$ of all rational 
 points in $S^1$. We give a complete description of an initial discrete par
 t of the Lagrange spectrum of $S^1$ in the sense of intrinsic Diophantine 
 approximation. This is an analogue of the classical result of Markoff in 1
 879\, where he characterized the most badly approximable real numbers via 
 the periods of their continued fraction expansions. Additionally\, we pres
 ent similar results for a few different subsets $Z$ of $S^1$. This is join
 t work with Dong Han Kim.\n
LOCATION:https://researchseminars.org/talk/NEDNT/8/
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